Archimedes Took a Bath Before

The best opportunities to learn are when we are perplexed, when we wonder.

Archimedes was born in 287 BC on the eastern coast of Sicily, in the city of Syracuse. He was a Greek mathematician, physicist, engineer, inventor, and astronomer. He was known for his obsessive pursuit to find the solution to nearly any problem he encountered. Among his resume of works is the Archimedes’ Screw used to pump water, a collection of enormous mirrors designed to burn ships at sea, the odometer, and systems to fire catapults more accurately. Despite the meatiness of his resume, Archimedes is most remembered for taking a bath.

King Hiero II of Sicily had commissioned a goldsmith to make a votive crown, for which the King supplied the gold. When the goldsmith returned with the crown the King was suspicious that perhaps the goldsmith used some silver in place of the gold. So King Hiero II summoned Archimedes to investigate the contents of the crown but there was a catch; Archimedes was not allowed to damage the crown in any way. So he could not simply cut the crown in half or melt it down.

Archimedes knew that to solve the problem he had to determine the density of the crown. He also knew that density was a measurement of an objects mass divided by its volume. Mass was easy for Archimedes to determine, he simply put it on a scale, afterall silver weighs less than gold. When he did this he saw that the crown’s weight was correct which meant that either the crown was entirely gold, or the goldsmith used more silver to match. To test the latter Archimedes would need to determine the volume of the crown; this was the tricky part. A crown is an irregular object. You can’t measure its sides like a box or its circumference like a sphere.

Late in the evening, while contemplating the problem Archimedes decided to take a bath and then retire for the evening. As he lowered himself into the tub he noticed that when he sat in the bath the waterline rose. The more of his body he lowered in, the more water would rise. Archimedes realized that this was the key to solving the puzzle. The displaced water was the exact volume of anything lowered into the tub.

This discovery excited Archimedes so much that he ran through the streets naked, dripping of his bath water, and shouting “eureka”, which is Greek for “I found it”. By lowering the crown in water he would be able to measure the crown’s volume compared to an equal amount of gold. Archimedes now knew the volume of the crown and concluded that the King was cheated out of his gold.

Why I love this story is because Archimedes took baths before this day. This wasn’t his first bath he had taken. He had been literally immersed in this solution thousands of times before. The question made him find the answer. The question made him realize that his bathtub was the solution.

There are times when we play the role of King Heiro II giving the opportunity to others to take the stage as Archimedes. We do this by asking questions that help people rethink their bath. Whether people are looking to triple their sales, grow their community, or just implement a simple idea; the right questions will help them see the answers that have been sitting right in front of them all along. Other times we have to play the role of Archimedes, challenged to look at what we have in a new way. Finding the solution within our own walls.

When are you King Heiro II, and when are you Archimedes?


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